 Skew-Hermitian matrix

A complex matrix $A$ is skew-Hermitian when $A^{†}=-A$. Its matrix exponential $e^{tA}$ is unitary for every real $t$.

A Skew-Hermitian matrix, also known as an anti-Hermitian matrix, is a square matrix \( A \) defined by the property: \[ A^* = -A \] where \( A^* \) is the conjugate transpose (also known as the Hermitian transpose) of the matrix \( A \).